1 edition of Abstract Convexity and Global Optimization found in the catalog.
This book consists of two parts. Firstly, the main notions of abstract convexity and their applications in the study of some classes of functions and sets are presented. Secondly, both theoretical and numerical aspects of global optimization based on abstract convexity are examined. Most of the book does not require knowledge of advanced mathematics. Classical methods of nonconvex mathematical programming, being based on a local approximation, cannot be used to examine and solve many problems of global optimization, and so there is a clear need to develop special global tools for solving these problems. Some of these tools are based on abstract convexity, that is, on the representation of a function of a rather complicated nature as the upper envelope of a set of fairly simple functions. Audience: The book will be of interest to specialists in global optimization, mathematical programming, and convex analysis, as well as engineers using mathematical tools and optimization techniques and specialists in mathematical modelling.
|Statement||by Alexander Rubinov|
|Series||Nonconvex Optimization and Its Applications -- 44, Nonconvex optimization and its applications -- 44.|
|LC Classifications||QA315-316, QA402.3, QA402.5-QA402.6|
|The Physical Object|
|Format||[electronic resource] /|
|Pagination||1 online resource (xviii, 493 p.)|
|Number of Pages||493|
|ISBN 10||1441948317, 1475732007|
|ISBN 10||9781441948311, 9781475732009|
The purpose of this paper is to extend Himmelberg's fixed point theorem replacing the usual convexity in topological vector spaces by an abstract topological notion of convexity which generalizes classical convexity as well as several metric convexity structures found in the literature. We prove the existence, under weak hypothese, of a fixed point for a compact approachable map and we provide Author: H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano, J.-V. Llinares. On Quasi-Convex Duality. Jean-Paul Penot, Michel Volle; Jean-Paul Penot, 18 August | Journal of Global Optimization, Vol. 40, No. Fenchel’s Duality Theorem for Nearly Convex Functions. Abstract Convexity. Generalized Convex Duality and its Economic blackfin-boats.com by:
A Tutorial on Convex Optimization Haitham Hindi Palo Alto Research Center (PARC), Palo Alto, California email: [email protected] Abstract—In recent years, convex optimization has be-come a computational tool of central importance in engi-neering, thanks to it’s ability to solve very large, practical engineering problems reliably and blackfin-boats.com by: Discrete Convexity and its Application to Convex Optimization on Discrete Time Scales Aykut Arslan Western Kentucky University Department of Mathematics Bowling Green, , USA [email protected] Abstract In this paper, we discuss convexity on n-dimensional discrete time scales T = T 1 T 2 T.
Jul 02, · This is a very pleasant text on global optimization problems, concentrating on those problems that have some kind of convexity property. It describes itself as a Ph.D. level text, but in fact it is easy to read and develops all the necessary background, so it could be used by . In this paper we study two classes of sets, strongly and weakly convex sets. For each class we derive a series of properties which involve either the concept of supporting ball, an obvious extension of the concept of supporting hyperplane, or the normal cone to the blackfin-boats.com by:
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Abstract Convexity and Global Optimization. Authors: Rubinov, Alexander M. Free Preview. Buy this book eBook ,59 € 'This book, written by one of the leading contributors in the field, is an up-to-date and very valuable reference. It will be precious to any researcher working in the field on theoretical aspects and applications as well.
Abstract Convexity and Global Optimization (Nonconvex Optimization and Its Applications Book 44) - Kindle edition by Alexander M. Rubinov. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Abstract Convexity and Global Optimization (Nonconvex Optimization and Its Applications Book 44).Cited by: Get this from a library.
Abstract Convexity and Global Optimization. [Alexander Rubinov] -- This book consists of two parts. Firstly, the main notions of abstract convexity and their applications in the study of some classes of functions and sets are presented.
Secondly, both theoretical. Abstract convexity and global optimization. [Aleksandr Moiseevich Rubinov] Home. WorldCat Home Abstract Convexity and Global Optimization book WorldCat Help.
Search. Search for Library Items Search for Lists Search for 'This book, written by one of the leading contributors in the field, is an up-to-date and very valuable reference. However, local approximation alone cannot help to solve many problems of global optimization, so there is a clear need to develop special global tools for solving these problems.
The simplest and most well-known area of global and simultaneously local optimization is convex programming. Buy Abstract Convexity and Global Optimization (Nonconvex Optimization and Its Applications) on blackfin-boats.com FREE SHIPPING on qualified orders.
Abstract. In this paper we study the emerging area of abstract convexity. The theory of abstract convex functions and sets arises out of the properties of convex functions related to their global nature. One of the main applications of abstract convexity is global optimization.
May 31, · Buy Abstract Convexity and Global Optimization by Alexander M. Rubinov from Waterstones today. Click and Collect from your local Waterstones Book Edition: Ed. Abstract convexity and non-smooth analysis.
Abstract Convexity and Global Optimization. Article. Jan ; A. Rubinov and results concerning invariant sets in control and it is the core.
The theory of abstract convexity generalizes ideas of convex analysis by using the notion of global supports and the global definition of subdifferential. In order to apply this theory to optimization, we need to extend subdifferential calculus and separation properties into the area of abstract convexity.
In the final part of the book we shall discuss possible applications of abstract convexity to global optimization. Some elements of theory of global optimization will be discussed in this chapter.
An updated and revised edition of the title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces.
The main emphasis is on applications to convex optimization and. Find many great new & used options and get the best deals for Abstract Convexity and Global Optimization by Alexander M. Rubinov (Paperback, ) at the best online prices at eBay. Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex blackfin-boats.com classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Convex optimization has applications in a wide range of disciplines, such as automatic control systems, estimation and.
We study augmented Lagrangians in a very general setting and formulate the main definitions and facts describing the augmented Lagrangian theory in terms of abstract convexity tools. We illustrate our duality scheme with an application to stochastic semi‐infinite blackfin-boats.com by: Mathematical Optimization and Economic Theory.
Abstract. No abstract available. Rubinov A and Andramonov M () Minimizing Increasing Star-shaped Functions Based on Abstract Convexity, Journal of Global Optimization,(), Online publication date: 1-Jul This book consists of a collection of research papers based on results presented during the conference and are dedicated to Professor Hoang Thy on the occasion of his 70th birthday.
The papers cover a wide range of recent results in Mathematical Pro gramming. Abstract Convexity and Global Optimization. Special tools are required for. Based on the book “Convex Optimization Theory,” Athena Scientiﬁc, of Athena Scientific, and are used with permission.
LECTURE 1 AN INTRODUCTION TO THE COURSE LECTURE OUTLINE •The Role of Convexity in Optimization •Duality Theory Convex Analysis and Optimization.
Spring For information about citing these materials. We present a global optimization algorithm for MINLPs (mixed-integer nonlinear programs) where any non-convexity is manifested as sums of non-convex univariate functions.
The algorithm is implemented at the level of a modeling language, and we have had substantial success Cited by: 7. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework.
The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. Abstract Convexity And Global Optimization By Alexander Rubinov Auth please fill out registration form to access in our databases.
Summary: Abstract convexity and global optimization by alexander rubinov auth pages isbn djvu 4 mb special tools are required for examining and.Downloadable (with restrictions)! In this paper, we first obtain some properties of topical (increasing and plus-homogeneous) functions in the framework of abstract convexity.
Next, we use the Toland–Singer formula to characterize the dual problem for the difference of two topical functions. Finally, we present necessary and sufficient conditions for the global minimum of the difference of.Abstract Copositivity plays an important role in optimization, particularly in discrete and quadratic optimization, since many of these problems admit a conic reformulation, or, at least, a re-laxation over the completely positive cone and by duality we obtain a related conic problem over the copositive cone.